STATISTICS

Standard Deviation

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Date Published:	August 2, 2019
Last Modified:	August 2, 2019

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Overview

The standard deviation is a metric which is used to measure the amount of variation in a set of data values.

The standard deviation has the same units as the data.

Equation

$$ \sigma = \sqrt{\frac{ \sum{(x - \bar{x})?^2}}{n}} $$

where:
$ \bar{x} $ is the mean (average) of the samples
$ n $ is the number of samples

For example,

4, 8, 7, 3, 12

\begin{align} \bar{x} &= \frac{1}{5} * (4+8+7+3+12)\\ &= 6.8\\ \\ \sum{(x - \bar{x})} = (4-6.8)^2+(8-6.8)^2+(7-6.8)^2+(3-6.8)^2+(12-6.8)^2\\ = \end{align}

Software

You can calculated the standard deviation of an array in Numpy with np.std():

1
np.std(my_array)

By default, the array is flattened. However, you can specify an axis on which to calculate the standard deviation.

Authors

Geoffrey Hunter

Dude making stuff.

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This work is licensed under a Creative Commons Attribution 4.0 International License .